Machine Learning - Gradient Descent

This article explains what Gradient Descent is on Machine Learning.

What is Gradient Descent? #

Gradient Descent is arguably the backbone of machine learning. It’s a first-order iterative optimization algorithm used to find the minimum value of a function. Simply put, it’s a method for finding the lowest point of a curve. But in the context of machine learning, it’s how we train our models to make accurate predictions. Let’s break this down.

The Intuition #

Imagine you’re blindfolded on a mountain, and your goal is to get to the bottom as quickly as possible. You can feel the slope of the mountain under your feet and decide your next step based on the steepest descent. This is what Gradient Descent does in a mathematical landscape.

The Cost Function #

The mountain in our scenario is the cost function, a measure of “how bad” the model is based on its parameters. For a linear regression model, it’s the mean squared error over all training examples. The goal is to adjust the parameters to minimize this error.

The Gradients #

The slope you feel under your feet are the gradients. In mathematical terms, a gradient is a partial derivative with respect to its inputs. In simpler terms, it tells you how much the cost function will change if you change the parameters slightly.

The Descent #

Here’s how it works:

1. Initialize Parameters: Start with random values for the parameters.
2. Calculate Gradient: Determine the gradient of the cost function at the current position.
3. Update Parameters: Adjust the parameters in the opposite direction of the gradient.
4. Repeat: Perform steps 2 and 3 until the cost function stops changing significantly.

This iterative process is the descent down the mountain, and it’s done over several iterations or epochs until we reach convergence.

Learning Rate #

The size of the steps you take is called the learning rate. If it’s too small, you’ll eventually reach the bottom, but it might take a long time. If it’s too large, you might overshoot and never reach the bottom. Finding the right learning rate is crucial and often requires some experimentation.

Types of Gradient Descent #

There are a few different flavors of Gradient Descent:

• Batch Gradient Descent: Uses the entire training set to calculate the gradient at each step.
• Stochastic Gradient Descent (SGD): Uses a single training example at each step. It’s much faster and can escape local minima, but it’s also noisier.
• Mini-batch Gradient Descent: Strikes a balance between Batch and SGD by using a subset of the training data for each step.

Challenges #

Gradient Descent isn’t without its challenges:

• Local Minima: These are “valleys” in the cost function that aren’t the absolute lowest point.
• Plateaus: Flat areas where the gradient is close to zero can slow down the descent.
• Choosing the Right Learning Rate: As mentioned, this is crucial and can be tricky.

Conclusion #

Gradient Descent is a fundamental algorithm in machine learning for optimizing models. It’s how we “train” our models to make better predictions. Understanding how it works is key to understanding how machine learning algorithms learn from data.

Remember, like many methods in machine learning, Gradient Descent is more of an art than a science. It requires intuition, experimentation, and practice to master.